Answer:
5.846∠-25.704°
Explanation:
The sum is easily found using an appropriate calculator.
2∠30° +5∠-45° ≈ 5.846∠-25.704°
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sum using rectangular coordinates
If you have a less-capable calculator, you can add the rectangular coordinates and convert the result to polar form
2∠30° +5∠-45° = (2cos(30°), 2sin(30°) +(5cos(-45°), 5sin(-45°))
= (√3, 1) +(5/2√2, -5/2√2) = (5/2√2 +√3, 1 -5/2√2)
The magnitude is the root of the sum of squares of these values:
|sum| = √(29+5(√6 -√2)) ≈ 5.846
The angle is the arctangent of the ratio of the second value to the first.
∠sum = arctan((1 -5/2√2)/(5/2√2 +√3)) ≈ -25.704°
Then the sum of the two numbers is about 5.846∠-25.704°.